Topological solvability and index characterizations for a common DAE power system model

Abstract

For the widely-used power system model consist- ing of the generator swing equations and the power flow equa- tions resulting in a system of differential algebraic equations (DAEs), we introduce a sufficient and necessary solvability condition for the linearized model. This condition is based on the topological structure of the power system. Furthermore we show sufficient conditions for the linearized DAE-system and a nonlinear version of the model to have differentiation index equal to one. Index Terms— Differential algebraic equations, power sys- tems, regularity, differentiation index. I. INTRODUCTION The integration of an increasing number of renewable energy sources makes it necessary to analyze and simu- late sophisticated dynamical models of power grids. One common model of power grids on the transmission level is the combination of the generator swing equations with the nonlinear power balance equation resulting in a nonlinear differential algebraic equation (DAE). Solvability of nonlin- ear (as well as linear) DAEs is in general not guaranteed and can often only be checked ad hoc for the specific given DAE when parameter values are known. In this paper we present a characterization of solvability solely in terms of the topology of the power network for the linearized DAE model. For numerical simulation the differentiation index, which we will shortly call index, of a DAE plays a crucial role and we also show that any solvable linearized DAE model of the power system is index one. Furthermore, we extend this index one characterization to a simplified nonlinear DAE model. There